Problem: The grades on a language midterm at Oak are normally distributed with $\mu = 74$ and $\sigma = 4.5$. Omar earned a n $88$ on the exam. Find the z-score for Omar's exam grade. Round to two decimal places.
Answer: A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for Omar's exam grade by subtracting the mean $(\mu)$ from his grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{88 - {74}}{{4.5}}} $ ${ z \approx 3.11}$ The z-score is $3.11$. In other words, Omar's score was $3.11$ standard deviations above the mean.